Abstract
Let k, m be positive integers and F-2m be a finite field of order 2(m) of characteristic 2. The primary goal of this paper is to study the structural properties of cyclic codes over the ring S-k = F-2m[v(1),v(2),...,v(k)]/< v(i)(2)-alpha(i)v(i),v(i)v(j)-v(j)v(i)>, for i, j = 1, 2, 3,..., k, where alpha(i) is the non-zero element of F-2m. As an application, we obtain better quantum error correcting codes over the ring S-1 (for k = 1). Moreover, we acquire optimal linear codes with the help of the Gray image of cyclic codes. Finally, we present methods for reversible DNA codes.